Closed form solutions to the stress analysis for an elastic coil of superconducting magnets, which include isotropic Green's functions solution and orthotropic generalized plane strain analysis, are presented. The prediction of stress and strain is essential for both mechanical and electrical design of high field superconducting magnets. The generalized plane strain analysis provides an analytical formulation for the axisymmetric state of stress and strain in the midplane of a superconducting magnet, where shear stress is negligible. This formulation takes into account the effect of the axial body force. The full axisymmetric stress analysis in terms of Green's functions provides the components of stress throughout the coil and includes the shear stress in addition to the normal stresses. Green's functions method permits the development of a solution irrespective of the type of the field or its distribution within the coil. Green's functions are derived by using finite integral transforms in an interval appropriate for a coil, e.g., finite Hankel transform. A comparison of the analytical results with the finite element methods is presented to confirm the validity of the solutions. The results show good agreement for both generalized plane strain analysis and Green's functions solution with the results of finite element methods.
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